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Finite X/A: Unit 6 Day 1. Demonstrate an Understanding of Concepts. Addition, Subtraction & Multiplication by a Scalar. Matrix. Football Stats Matrix. Definition of a Matrix. - PowerPoint PPT Presentation
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Demonstrate an Understanding of
ConceptsAddition, Subtraction &
Multiplication by a Scalar
Finite X/A: Unit 6 Day 1
Matrix
Eagles Saints
Rush Yards 112 118Pass Yards 225 284Total Yards 337 402Turnovers 2 2Time of Pos. 33:03 27:57
Football Stats Matrix
Eagles Saints
Rush Yards 112 118Pass Yards 225 284Total Yards 337 402Turnovers 2 2Time of Pos. 33:03 27:57
112 118
225 284
337 402
2 2
33: 03 27 :57
Definition of a Matrix
• An m by n matrix is a rectangular array of elements arranged in m rows and n columns such that it can be written as…
11 12 1
21 22 1
1 1
...
...
...
n
n
m m mn
a a a
a a aA
a a a
Dimensions of a Matrix
• Listed as...
Row x Column
Equal Matrices
• Two matrices are equal if…– They have the same dimension– They have the same exact numbers in all
corresponding positions
Equal or not equal?
4 2
1 8
5 0
4 1 5
2 8 0
Adding Matrices
• Matrices can only be added if…
• To add them, add each number in the corresponding position and then write the sum in that corresponding position of the new matrix.
Adding Matrices Example
8 1
5 14 0 2
1
2 7
430
17
9 4
5 4
2
Multiplication by a Scalar
• As we saw before, matrices are denoted by capital letters.
• Sometimes you will see a problem like this…
, Find 3A.
This is called scalar multiplication
2 1
0 4A
How to Multiply by a Scalar
• To perform scalar multiplication, multiply every element of the matrix by the scalar
2 1 6 33
0 4 0 12A A
More Scalar Multiplication
• You may also see matrices written as such…
This still means scalar
multiplication…
Multiply by 4
4 2
4 2 5
0 8
Subtracting Matrices…
• To subtract matrices, combine scalar multiplication with matrix addition…
5 2 3 4 1 8
5 2 3 1 4 1 8
5 2 3 4 1 8
5 4 2 1 3 8 1 3 11
Closure
• What is/are…– A (the) Matrix?– The dimensions of a matrix?– Equal Matrices?– Matrix Addition and Subtraction?– Scalar Multiplication?